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EAST RUTHERFORD, N.J. (AP) — Rex Ryan was brash and confident all week, insisting his Jets were the kings of New York.

Well, the Giants shut him up in a big way — taking the city bragging rights and setting up an even more important showdown with the Dallas Cowboys next weekend with a 29-14 victory Saturday.

“I hate to use that cliche, but this is a huge one,” left tackle David Diehl said. “This is about the city, the city of New York and what team wants to be responsible. They have talked all week and said what they wanted to say. From Day 1, they’re our big brother and other stuff. We went out there and played our game and showed whose stadium this is.”

Ryan said the Jets were the better team the last two years, based on their consecutive trips to the AFC championship game and the Giants missing the postseason. Tom Coughlin responded by saying, “Talk is cheap. Play the game.”

It was the Giants who did.

“They were the better team today, and they’re the better team this year,” a humbled Ryan said. “Clearly, I was wrong.”

The Giants kept their postseason hopes alive, helped by Victor Cruz setting two franchise receiving records and Ahmad Bradshaw running for two touchdowns. While neither team looked much like playoff material, the Giants (8-7) are now in position to win the NFC East with a victory at home next Sunday against Dallas.

“Given everything that was at stake, and all the noise that has been coming out of Florham Park,” Giants co-owner John Mara said, “yeah, it means a little more.”

Running back Brandon Jacobs said he had an exchange with Ryan after the game in which the coach approached him, used an expletive and said, “Wait till we win the Super Bowl.”

Added Jacobs: “And I told him I’ll punch him in the face. I told him out of all these Giants players on this team you’re talking to the wrong one. And that was that.”

Ryan acknowledged that he and Jacobs “had a private conversation. He doesn’t like me; I respect him.”

The back-and-forth went on even in the hours before the game, when Jacobs and kicker Lawrence Tynes both removed black curtains placed by the Jets over the Giants’ Super Bowl logos. The Jets said it was simply their standard practice to cover those logos for every one of the team’s home games, regardless of opponent, because it is the players’ entrance.

“We knew early what we were going to get no matter what happened as soon as he had the opportunity to run his big fat mouth,” Jacobs said of Ryan’s boasts throughout the week.

Meanwhile, the Jets’ playoff hopes took a devastating hit, and at 8-7 they’ll need to win at Miami next week and get major help from several other teams. They have to hope for Cincinnati and Tennessee to lose, and have either Oakland or Denver lose.

“I mean, we don’t deserve to control our own destiny,” Jets linebacker Bart Scott said. “We haven’t played good enough football to do that. We need to try to finish strong, but if you don’t make it to the playoffs, you’ve got nobody to blame but yourself.”

Cruz, who had three catches for 164 yards, broke Amani Toomer’s single-season mark for yards receiving — and the team’s record for longest touchdown reception, a 99-yarder that gave the Giants the lead for good in the second quarter.

“It’s just amazing,” Cruz said, “and to beat the Jets in the process is added incentive.”

It was a brutal game at times, with both offenses sluggish and prone to mistakes. The Jets were also penalized 10 times, including a late hit call on Aaron Maybin, who plowed into D.J. Ware in the fourth quarter — a play on which Coughlin was injured out of bounds. The Giants coach needed to be checked out on the bench briefly before limping back to the sideline.

“Never better,” a smiling Coughlin said when asked how he was feeling.

Eli Manning finished just 9 of 27 for 225 yards. Mark Sanchez completed 30 passes on a career-high 59 attempts but put up only 258 yards and was intercepted twice. The Jets were also a brutal 4 for 21 on third-down conversions.

“I left a lot of completions out there,” Sanchez said.

The sloppiest stretch came midway through the fourth quarter with wild swings of momentum.

The Giants thought they had stopped the Jets on fourth down, but a pass interference call gave them new life. Plaxico Burress — playing against the Giants in the regular season for the first time since they cut him in 2009 and he served a 20-month prison sentence on a gun charge — thought he had scored a touchdown, but offensive pass interference called it back. The Giants thought they’d recovered a fumble by Sanchez, but officials reversed the call on a challenge, saying his arm was going forward.

The Giants got their turnover moments later, though, when Sanchez fumbled the snap in the end zone.

The Jets weren’t done. David Harris intercepted Manning’s pass that tipped off Hakeem Nicks’ hands, and the Jets had another apparent fumble by Sanchez reversed on review.

On third-and-12 from the 13, Sanchez scrambled for 11 yards — and Antrel Rolle was called for holding, putting the ball at the 1. Sanchez dived into the end zone, making it 20-14 with 7:17 left.

But the Jets wouldn’t get any closer. Chris Canty sacked Sanchez for a safety, and after an onside free kick by the Jets was recovered by the Giants, Bradshaw had a 19-yard TD run with 2:04 left.

“It’s real sad right now,” Jets cornerback Darrelle Revis said. “We needed this win. We made some mistakes and they outplayed us.”

Cruz’s 99-yard catch — the longest scoring pass in team history — came with the Giants in dire straits facing third-and-10 from the 1. Manning, standing in the back of the end zone, zipped a pass to Cruz, who dodged tackle attempts by Antonio Cromartie and Kyle Wilson and took off down the right sideline. Eric Smith was the only one with a chance to get him, but Cruz outran him to give the Giants a 10-7 lead with 2:12 left in the opening half.

It was also the longest offensive play against the Jets in team history.

Now the Jets will prepare for the Dolphins — and keep their fingers crossed.

Notes: DE Jason Pierre-Paul had two of the Giants’ five sacks, giving him 15½ this season. … Jets S Brodney Pool said he experienced migraine symptoms during the game, worsened after a hard hit in the third quarter when Bradshaw slammed into him. He said he was fine. … Jets LB Garrett McIntyre hurt his knee covering the opening kickoff, and there was no immediate word on the injury.